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Quadratic Forms in Infinite Dimensional Vector Spaces pp 61–95Cite as

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Diagonalization of א0-Forms

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Part of the book series: Progress in Mathematics ((PM,volume 1))

Abstract

In this chapter we shall prove that א0-dimensional sesquilinear spaces are orthogonal sums of lines and planes and we characterize the cases where a decomposition into mutually orthogonal lines is impossible. The problem of “normalizing” bases brings us to stability and the beginner is confronted with the first Ping-Pong style proof with its characteristic back-and-forth argument (Theorem 2). These matters are basic and their knowledge is tacitly assumed in the rest of the book.

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References to Chapter II

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References to Appendix I

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Authors and Affiliations

  1. Mathematisches Institut, Universität Zürich, Freiestrasse 36, CH-8032, Zürich, Switzerland

    Herbert Gross

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  1. Herbert Gross
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© 1979 Springer Science+Business Media New York

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Gross, H. (1979). Diagonalization of א0-Forms. In: Quadratic Forms in Infinite Dimensional Vector Spaces. Progress in Mathematics, vol 1. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3542-7_3

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  • DOI: https://doi.org/10.1007/978-1-4899-3542-7_3

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-0-8176-1111-8

  • Online ISBN: 978-1-4899-3542-7

  • eBook Packages: Springer Book Archive

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